Derivative Estimation from Coarse, Irregular, Noisy Samples: An MLE-Spline Approach
Methodology
2025-07-31 v1 Systems and Control
Systems and Control
Optimization and Control
Probability
Abstract
We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with -norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a non-standard parameterization of quadratic splines and develop recursive online algorithms. Two formulations -- quadratic and zero-order -- offer tradeoff between smoothness and computational speed. Simulations demonstrate superior performance over high-gain observers and super-twisting differentiators under coarse sampling and high noise, benefiting systems where higher sampling rates are impractical.
Cite
@article{arxiv.2507.22176,
title = {Derivative Estimation from Coarse, Irregular, Noisy Samples: An MLE-Spline Approach},
author = {Konstantin E. Avrachenkov and Leonid B. Freidovich},
journal= {arXiv preprint arXiv:2507.22176},
year = {2025}
}